Physics-Conditioned Diffusion Models for Lattice Gauge Theory

2025-02-08

AI Summary

To address topological freezing, inefficient cross-parameter/cross-scale sampling, and challenges in embedding physical constraints into generative models for lattice gauge theory simulations, this work introduces the first physics-constrained diffusion model. It incorporates stochastic quantization as a hard physical constraint directly into the denoising process and integrates Metropolis-adjusted Langevin dynamics (MALA) to ensure exact sampling. The method generalizes seamlessly—without retraining—to arbitrary coupling strengths (β) and lattice volumes. In the 2D U(1) lattice gauge theory, it achieves significantly improved sampling efficiency for the topological charge, outperforming both Hamiltonian Monte Carlo (HMC) and conventional Langevin approaches. Crucially, it enables reliable extrapolation from small-β regimes to the physically relevant large-β (weak-coupling) regime. The framework thus unifies high physical fidelity with computational scalability, offering a robust foundation for first-principles simulation of topologically nontrivial quantum field theories.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Diffusion Models for Vision

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in two spacetime dimensions and find that a model trained at a small inverse coupling constant can be extrapolated to larger inverse coupling regions without encountering the topological freezing problem. Additionally, the trained model can be employed to sample configurations on different lattice sizes without requiring further training. The exactness of the generated samples is ensured by incorporating Metropolis-adjusted Langevin dynamics into the generation process. Furthermore, we demonstrate that this approach enables more efficient sampling of topological quantities compared to traditional algorithms such as Hybrid Monte Carlo and Langevin simulations.

Problem

• Simulating lattice gauge theories
• Extrapolating trained models
• Efficient sampling of topological quantities

Innovation

• Incorporates stochastic quantization physically
• Extrapolates model without topological freezing
• Ensures exactness with Metropolis-adjusted dynamics